Which of the following is the solution to the equation
$5 x - (4 x - 7) (3 x - 5) = 6 - 3 (4 x - 9) (x - 1)$

- 2

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2

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4

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Solution

The correct option is C $2$
$5 x - (4 x - 7) (3 x - 5) = 6 - 3 (4 x - 9) (x - 1)$

$\Rightarrow 5 x - [4 x (3 x - 5) - 7 (3 x - 5)] = 6 - 3 [4 x (x - 1) - 9 (x - 1)]$

$\Rightarrow 5 x - [12 x^{2} - 20 x - 21 x + 35] = 6 - 3 [4 x^{2} - 4 x - 9 x + 9]$

$\Rightarrow 5 x - [12 x^{2} - 41 x + 35] = 6 - 3 [4 x^{2} - 13 x + 9]$

$\Rightarrow 5 x - 12 x^{2} + 41 x - 35 = 6 - 12 x^{2} + 39 x - 27$

$\Rightarrow 5 x - 12 x^{2} + 41 x - 35 - 6 + 12 x^{2} - 39 x + 27 = 0$

$\Rightarrow 7 x - 14 = 0$

$\Rightarrow 7 x = 14$

$\Rightarrow x = \frac{14}{7} = 2$

$∴ x = 2$

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